LITTLE ROCK — Heading into this year’s legislative session, opponents of Arkansas’ compromise Medicaid expansion vowed to push for an exit plan for a program they see as no different from the law they have been deriding simply as “Obamcare.”

Now, they may be the ones in need of an exit strategy.

With the impasse over Arkansas’ “private option” heading into its third week, opponents of the plan to use federal Medicaid funds to purchase insurance for the poor are looking for a way out of a showdown that could jeopardize the state’s budget.

Not to mention the Republican Party’s efforts to build on their recent gains.

The latest compromise being floated as a way to get to the 75 votes needed — a proposal to limit the signup period for the private option - is an acknowledgement by some opponents of the program that they don’t have the numbers to force its dismantling during this year’s session.

“What we would like to do is slow it down. ... We know we just can’t kill it,” said Rep. Bruce Cozart, R-Hot Springs, who had been among a handful of private option opponents meeting with House leaders about a potential compromise.

Crafted as an alternative to expanding Medicaid under the federal health care law, the private option has been touted as a model for Republicans in other states to implement a key part of the law they’ve campaigned against for the past two election cycles. Nearly 94,000 Arkansans are receiving subsidized coverage through the program.

The Senate has voted to reauthorize the program, but the legislation has stalled in the House after failing four times to receive the 75 votes needed to continue the program.

The uncertainty over the program’s future threatens to spill into other parts of the state’s budget.

Democratic Gov. Mike Beebe has said that $89 million of his proposed $5 billion budget depends on savings expected by the private option cutting down on hospitals’ unpaid bills.

House Speaker Davy Carter backed off his plans for daily votes on the program’s future last week, challenging opponents of the program to offer an alternative that could win the three-fourths support needed in both chambers.

“If somebody else has got a better idea, then I want to see it,” Carter, R-Cabot, told reporters.

“Instead of complaining about the idea that three-fourths of the Senate has and so far the vast majority of the House members have. Just produce it. There’s nothing.”

The main alternatives floated by opponents so far — pulling the private option out of the Medicaid budget or winding the program down by early next year — have been dismissed by supporters as non-starters since they kill the very program they’re trying to save.

“I think we’ve been trying to talk about what could be acceptable to a supermajority of the House,” said House Majority Leader Bruce Westerman, R-Hot Springs, a chief opponent of the program.

The key to breaking that stalemate may be a proposal to create a limited enrollment period for the private option, rather than allow signups throughout the year.

The plan floated by a handful of the opponents to the program wouldn’t require a change in the legislation, and instead would rely on the state seeking federal approval for the enrollment limitation.

It would address a key concern by supporters of the program, who say they’re unwilling to negotiate any more changes to the private option funding bill after adding amendments aimed at swaying opponents of the program.

Those amendments include a prohibition against spending any public funds to promote the private option or other parts of the federal health law.

Those changes were pitched by an opponent of the private option, who acknowledged that the votes weren't there to kill the program this session but said they'd at least slow the growth in the program.

"I did my best to provide what I believed was a way out of this impasse. and here we are," said Rep. Nate Bell, R-Mena, who had proposed the advertising prohibition.

The standoff has tested the patience of Democrats, who vented frustration over the back-to-back failed votes after grudgingly agreeing to the amendments.

It's also continuing to sharply divide Republicans and ensuring the private option will be a wedge issue in dozens of GOP primary fights throughout the state this spring.

The looming shadow of the election may ultimately be the bigger factor in whether the private option survives than any other changes to the program.

With the filing period for state and federal offices ending at noon Monday, it's a shadow that may fade enough for a breakthrough by the time the House takes up the measure again.

Andrew DeMillo has covered Arkansas government and politics for The Associated Press since 2005.